If you can maintain a 50% win rate, you'll be able to unlock "Breaking Records" and "Over The Top!" at around the same time. These two achievements shouldn't be a problem if you plan on playing this game for a long time.
If you just want the achievements with as little time and effort as possible, find a player in the Achievement Trading Thread to boost with in a private match. Take turns letting each other win over the course of 200 matches and you should be able to unlock both achievements at the same time.
When it says 'complete' matches, it appears that you do need to play through the entire match. Wins/matches from disconnects will not count towards the achievements. If you find you've reached the required number of matches and haven't unlocked the achievement, try jumping into a few more matches until it pops.